They would only comment on a live and politically-charged issue if the Government of the day wished them to. Whether that's riots, other disturbances, or whatever.
I think you're perhaps getting muddled up with statements in the wake of disasters or acts of terrorism, and those usually focus on condolences for those affected, praise for emergency services and (possibly later, eg in Christmas message) on communities coming together.
I think the Prime Minister has made a good judgement call in following the 2011 precedent.
And I note that BBC is reporting that criticism for KC on this stems from the anti-monarchy group Republic. Balanced by commentary from the historian and Blair crony Seldon:
"Now is not the right time for the King to become involved.
"He is head of state, and it’s appropriate that while the crisis is going on, the head of government, the prime minister, handles the crisis management and says what is needed to be said.
"The time for the King to speak, if at all, is when everything has calmed down again. The issues that have led the riots are not going to go away quickly. We need to hear his considered thoughts then about societal harmony,"